Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (6): 1679-1688.

• Articles • Previous Articles     Next Articles

Exponential Inequalities for Negatively Associated Random Variables

  

  1. Department of Mathematics, Hunan University of Science and Engineering, Hunan |Yongzhou 425100
  • Received:2007-12-29 Revised:2008-12-23 Online:2009-12-25 Published:2009-12-25
  • Supported by:

    国家自然科学基金 (10161004)资助

Abstract:

The authors show some exponential inequalities for negatively associated random variables. These inequalities improve the rresponding results which Jabbari and Azarnoosh (2007) and Oliveira (2005) got. As an application, the authors obtain the rate of convergence n-1/2(log log n)1/2(log n)2 for the case of geometrically decreasing covariances, which closes to the optimal achievable convergence rate for independent random variables under an iterated logarithm, while Jabbari and Azarnoosh (2007) only got n-1/3(log n)5/3 for the case mentioned above.

Key words: Negatively associated random variable, Exponential inequality, Rate of convergence

CLC Number: 

  • 60F15
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